

D = 1;

sigma = 0.1;
N = 5:200;

epsilon = 2*pi*sigma./N;

v = 1./(D.*N) .* (-log(epsilon.*N./2) + N./8);

va = 1/(8*D) - 1/D .* epsilon./(pi*sigma) .* log(sin(pi*sigma/2));

plot(N,v,N,va);

hline = refline(0,1/(8*D));
set(hline,'color','r');

legend('Asymptotic','Homogeneous');
